H∞-optimal controller synthesis for dithered systems

In this paper a novel design algorithm is proposed to synthesize an H^∞-optimal observer-based controller for a multivariable system under multiplicative nonlinear time-varying perturbation. It is shown that optimal robustness and performance can both be attained, by using the technique of H^∞-optimization theory and by applying dither to smooth the nonlinearity. The exact solution of the model-matching problem induced by the stability criterion is solved by non-iterative computation method of H^∞-norm, allowing the optimal H^∞-controller to be expressed explicitly in terms of a free parameter, the dither amplitude, which is shown, here, as the dominant parameter on adjusting the gain of the H^∞-optimal controller in order to obtain high perfomances and to guarantee stability, simultaneously.